The teams exchanged chances during the second half – Ousmane Diakite nodding over for Albion and Wednesday’s Ike Ugbo having a low finish comfortably held by Griffiths.
And that trend continued when Baggies winger Johnston couldn’t quite find the bottom corner after cutting in, ahead of Owls player Yan Valery smashing a half-volley off-target.
Mason introduced Karlan Grant and Aune Heggebø to try and help earn his team the victory, but ultimately the scoreline remained level.
Albion: Griffiths, Gilchrist (Bielik 71), Phillips, Mepham (Dike 90+2), Styles (Taylor 71), Iling-Junior (Grant 60), Diakite, Mowatt, Johnston, Price (Heggebø 71), Maja.
Substitutes: Wildsmith, Deeming, Bany, Bostock.
Attendance: 23,622 (2,515).